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Journal of Visualized Experiments : JoVE Jan 2011Using the three-dimensional structure of biological macromolecules to infer how they function is one of the most important fields of modern biology. The availability of...
Using the three-dimensional structure of biological macromolecules to infer how they function is one of the most important fields of modern biology. The availability of atomic resolution structures provides a deep and unique understanding of protein function, and helps to unravel the inner workings of the living cell. To date, 86% of the Protein Data Bank (rcsb-PDB) entries are macromolecular structures that were determined using X-ray crystallography. To obtain crystals suitable for crystallographic studies, the macromolecule (e.g. protein, nucleic acid, protein-protein complex or protein-nucleic acid complex) must be purified to homogeneity, or as close as possible to homogeneity. The homogeneity of the preparation is a key factor in obtaining crystals that diffract to high resolution (Bergfors, 1999; McPherson, 1999). Crystallization requires bringing the macromolecule to supersaturation. The sample should therefore be concentrated to the highest possible concentration without causing aggregation or precipitation of the macromolecule (usually 2-50 mg/mL). Introducing the sample to precipitating agent can promote the nucleation of protein crystals in the solution, which can result in large three-dimensional crystals growing from the solution. There are two main techniques to obtain crystals: vapor diffusion and batch crystallization. In vapor diffusion, a drop containing a mixture of precipitant and protein solutions is sealed in a chamber with pure precipitant. Water vapor then diffuses out of the drop until the osmolarity of the drop and the precipitant are equal (Figure 1A). The dehydration of the drop causes a slow concentration of both protein and precipitant until equilibrium is achieved, ideally in the crystal nucleation zone of the phase diagram. The batch method relies on bringing the protein directly into the nucleation zone by mixing protein with the appropriate amount of precipitant (Figure 1B). This method is usually performed under a paraffin/mineral oil mixture to prevent the diffusion of water out of the drop. Here we will demonstrate two kinds of experimental setup for vapor diffusion, hanging drop and sitting drop, in addition to batch crystallization under oil.
Topics: Crystallization; Crystallography, X-Ray; Diffusion; Proteins
PubMed: 21304455
DOI: 10.3791/2285 -
Advances in Experimental Medicine and... 2020Diffusion within bacteria is often thought of as a "simple" random process by which molecules collide and interact with each other. New research however shows that this... (Review)
Review
Diffusion within bacteria is often thought of as a "simple" random process by which molecules collide and interact with each other. New research however shows that this is far from the truth. Here we shed light on the complexity and importance of diffusion in bacteria, illustrating the similarities and differences of diffusive behaviors of molecules within different compartments of bacterial cells. We first describe common methodologies used to probe diffusion and the associated models and analyses. We then discuss distinct diffusive behaviors of molecules within different bacterial cellular compartments, highlighting the influence of metabolism, size, crowding, charge, binding, and more. We also explicitly discuss where further research and a united understanding of what dictates diffusive behaviors across the different compartments of the cell are required, pointing out new research avenues to pursue.
Topics: Bacteria; Biophysical Phenomena; Diffusion
PubMed: 32894475
DOI: 10.1007/978-3-030-46886-6_2 -
Biophysical Journal Apr 2022Biochemical specificity is critical in enzyme function, evolution, and engineering. Here we employ an established kinetic model to dissect the effects of reactant...
Biochemical specificity is critical in enzyme function, evolution, and engineering. Here we employ an established kinetic model to dissect the effects of reactant geometry and diffusion on product formation speed and accuracy in the presence of cognate (correct) and near-cognate (incorrect) substrates. Using this steady-state model for spherical geometries, we find that, for distinct kinetic regimes, the speed and accuracy of the reactions are optimized on different regions of the geometric landscape. From this model we deduce that accuracy can be strongly dependent on reactant geometric properties even for chemically limited reactions. Notably, substrates with a specific geometry and reactivity can be discriminated by the enzyme with higher efficacy than others through purely diffusive effects. For similar cognate and near-cognate substrate geometries (as is the case for polymerases or the ribosome), we observe that speed and accuracy are maximized in opposing regions of the geometric landscape. We also show that, in relevant environments, diffusive effects on accuracy can be substantial even far from extreme kinetic conditions. Finally, we find how reactant chemical discrimination and diffusion can be related to simultaneously optimize steady-state flux and accuracy. These results highlight how diffusion and geometry can be employed to enhance reaction speed and discrimination, and similarly how they impose fundamental restraints on these quantities.
Topics: Diffusion; Kinetics; Ribosomes
PubMed: 35278424
DOI: 10.1016/j.bpj.2022.03.005 -
Proceedings of the National Academy of... Aug 2023Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabási-Albert models, among others....
Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabási-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing the network's connectivity, also might yield several undesired navigational effects: They tend to be overused during geodesic navigational processes-making the networks fragile-and provide suboptimal routes for diffusive-like navigation. Why, then, networks with complex topologies are ubiquitous? Here, we unveil that these models also entropically generate network bypasses: alternative routes to shortest paths which are topologically longer but easier to navigate. We develop a mathematical theory that elucidates the emergence and consolidation of network bypasses and measure their navigability gain. We apply our theory to a wide range of real-world networks and find that they sustain complexity by different amounts of network bypasses. At the top of this complexity ranking we found the human brain, which points out the importance of these results to understand the plasticity of complex systems.
Topics: Humans; Brain; Diffusion
PubMed: 37490534
DOI: 10.1073/pnas.2305001120 -
Journal of Biological Physics Sep 2023We present an analysis of an epidemic spreading process on an Apollonian network that can describe an epidemic spreading in a non-sedentary population. We studied the...
We present an analysis of an epidemic spreading process on an Apollonian network that can describe an epidemic spreading in a non-sedentary population. We studied the modified diffusive epidemic process using the Monte Carlo method by computational analysis. Our model may be helpful for modeling systems closer to reality consisting of two classes of individuals: susceptible (A) and infected (B). The individuals can diffuse in a network according to constant diffusion rates [Formula: see text] and [Formula: see text], for the classes A and B, respectively, and obeying three diffusive regimes, i.e., [Formula: see text], [Formula: see text], and [Formula: see text]. Into the same site i, the reaction occurs according to the dynamical rule based on Gillespie's algorithm. Finite-size scaling analysis has shown that our model exhibits continuous phase transition to an absorbing state with a set of critical exponents given by [Formula: see text], [Formula: see text], and [Formula: see text] familiar to every investigated regime. In summary, the continuous phase transition, characterized by this set of critical exponents, does not have the same exponents of the mean-field universality class in both regular lattices and complex networks.
Topics: Humans; Computer Simulation; Algorithms; Epidemics; Models, Biological; Diffusion
PubMed: 37118345
DOI: 10.1007/s10867-023-09634-2 -
The European Respiratory Journal Jul 2022
Topics: Carbon Monoxide; Diffusion; Humans; Pulmonary Diffusing Capacity
PubMed: 35902101
DOI: 10.1183/13993003.00789-2022 -
Biochimica Et Biophysica Acta Oct 2016Cellular membranes are typically decorated with a plethora of embedded and adsorbed macromolecules, e.g. proteins, that participate in numerous vital processes. With... (Review)
Review
Cellular membranes are typically decorated with a plethora of embedded and adsorbed macromolecules, e.g. proteins, that participate in numerous vital processes. With typical surface densities of 30,000 proteins per μm(2) cellular membranes are indeed crowded places that leave only few nanometers of private space for individual proteins. Here, we review recent advances in our understanding of protein crowding in membrane systems. We first give a brief overview on state-of-the-art approaches in experiment and simulation that are frequently used to study crowded membranes. After that, we review how crowding can affect diffusive transport of proteins and lipids in membrane systems. Next, we discuss lipid and protein sorting in crowded membrane systems, including effects like protein cluster formation, phase segregation, and lipid droplet formation. Subsequently, we highlight recent progress in uncovering crowding-induced conformational changes of membranes, e.g. membrane budding and vesicle formation. Finally, we give a short outlook on potential future developments in the field of crowded membrane systems. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.
Topics: Cell Membrane; Diffusion; Membrane Lipids; Membrane Proteins; Molecular Conformation
PubMed: 26724385
DOI: 10.1016/j.bbamem.2015.12.021 -
Comparative Biochemistry and... Mar 2021The capillary bed constitutes the obligatory pathway for almost all oxygen (O) and substrate molecules as they pass from blood to individual cells. As the largest organ,... (Review)
Review
The capillary bed constitutes the obligatory pathway for almost all oxygen (O) and substrate molecules as they pass from blood to individual cells. As the largest organ, by mass, skeletal muscle contains a prodigious surface area of capillaries that have a critical role in metabolic homeostasis and must support energetic requirements that increase as much as 100-fold from rest to maximal exercise. In 1919 Krogh's 3 papers, published in the Journal of Physiology, brilliantly conflated measurements of muscle capillary function at rest and during contractions with Agner K. Erlang's mathematical model of O diffusion. These papers single-handedly changed the perception of capillaries from passive vessels serving at the mercy of their upstream arterioles into actively contracting vessels that were recruited during exercise to elevate blood-myocyte O flux. Although seminal features of Krogh's model have not withstood the test of time and subsequent technological developments, Krogh is credited with helping found the field of muscle microcirculation and appreciating the role of the capillary bed and muscle O diffusing capacity in facilitating blood-myocyte O flux. Today, thanks in large part to Krogh, it is recognized that comprehending the role of the microcirculation, as it supports perfusive and diffusive O conductances, is fundamental to understanding skeletal muscle plasticity with exercise training and resolving the mechanistic bases by which major pathologies including heart failure and diabetes cripple exercise tolerance and cerebrovascular dysfunction predicates impaired executive function.
Topics: Animals; Capillaries; Diffusion; Humans; Muscle Cells; Muscles; Oxygen
PubMed: 33242636
DOI: 10.1016/j.cbpa.2020.110852 -
International Journal of Molecular... Nov 2023Using the framework of a continuous diffusion model based on the Smoluchowski equation, we analyze particle dynamics in the confinement of a transmembrane nanopore. We... (Review)
Review
Using the framework of a continuous diffusion model based on the Smoluchowski equation, we analyze particle dynamics in the confinement of a transmembrane nanopore. We briefly review existing analytical results to highlight consequences of interactions between the channel nanopore and the translocating particles. These interactions are described within a minimalistic approach by lumping together multiple physical forces acting on the particle in the pore into a one-dimensional potential of mean force. Such radical simplification allows us to obtain transparent analytical results, often in a simple algebraic form. While most of our findings are quite intuitive, some of them may seem unexpected and even surprising at first glance. The focus is on five examples: (i) attractive interactions between the particles and the nanopore create a potential well and thus cause the particles to spend more time in the pore but, nevertheless, increase their net flux; (ii) if the potential well-describing particle-pore interaction occupies only a part of the pore length, the mean translocation time is a non-monotonic function of the well length, first increasing and then decreasing with the length; (iii) when a rectangular potential well occupies the entire nanopore, the mean particle residence time in the pore is independent of the particle diffusivity inside the pore and depends only on its diffusivity in the bulk; (iv) although in the presence of a potential bias applied to the nanopore the "downhill" particle flux is higher than the "uphill" one, the mean translocation times and their distributions are identical, i.e., independent of the translocation direction; and (v) fast spontaneous gating affects nanopore selectivity when its characteristic time is comparable to that of the particle transport through the pore.
Topics: Nanopores; Diffusion
PubMed: 37958906
DOI: 10.3390/ijms242115923 -
The Journal of General Physiology Oct 2023Osmosis is an important force in all living organisms, yet the molecular basis of osmosis is widely misunderstood as arising from diffusion of water across a membrane...
Osmosis is an important force in all living organisms, yet the molecular basis of osmosis is widely misunderstood as arising from diffusion of water across a membrane separating solutions of differing osmolarities, and hence different water concentrations. In 1923, Peter Debye proposed a physical model for a semipermeable membrane emphasizing the repulsive forces between solute molecules and membrane that prevent the solute from entering the membrane. His work was hardly noticed at the time and slipped out of view. We show that Debye's analysis of van 't Hoff's law for osmotic equilibrium also provides a consistent and plausible mechanism for osmotic flow. A difference in osmolyte concentrations in solutions separated by a semipermeable membrane leads to different pressures at the two water-membrane interfaces because the total repulsive force between solute molecules and the membrane is different at the two interfaces. Water is therefore driven through the membrane for exactly the same reason that pure water flows in response to an imposed hydrostatic pressure difference. In this paper, we present the Debye model in both equilibrium and flow conditions. We point out its applicability regardless of the nature of the membrane with examples ranging from the predominantly convective flow of water through synthetic membranes and capillary walls to the purely diffusive flow of independent water molecules through a lipid bilayer and the flow of a single-file column of water molecules in narrow protein channels.
Topics: Diffusion; Lipid Bilayers; Osmosis; Pressure; Water
PubMed: 37624228
DOI: 10.1085/jgp.202313332